In contrast, after current annealing the mean free path in S1 increases to \(\sim \)  1 \(\mu \) m, comparable to the device dimensions of \(\sim \) 2 \(\mu \) m and transport is no longer diffusive. To elucidate the actual transport conditions in our sample we compare \(\sigma (n)\)  with the expectation from the extreme opposite position of purely ballistic propagation. There, the current is carried by the finite number of longitudinal modes \(N=Wk_F/\pi \) , where \(W\)  is the width of the sample. Assuming perfect transmission, the ballistic conductance at vanishing \(T\)  is given by [1]}, [2]}
\(\sigma _{bal}(n) = \frac{4e^2}{h}N = \frac{4e^2}{h}\frac{Wk_F}{\pi } \propto \sqrt{n}\) 
